Convolutional neural network architecture for geometric matching

We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are three-fold. First, we propose a convolutional neural network architecture for geometric matching. The architecture is based on three main components that mimic the standard steps of feature extraction, matching and simultaneous inlier detection and model parameter estimation, while being trainable end-to-end. Second, we demonstrate that the network parameters can be trained from synthetically generated imagery without the need for manual annotation and that our matching layer significantly increases generalization capabilities to never seen before images. Finally, we show that the same model can perform both instance-level and category-level matching giving state-of-the-art results on the challenging Proposal Flow dataset.Comment: In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017

Subspace procrustes analysis

Postprint (author's final draft

Higgs and Coulomb branches from vertex operator algebras

We formulate a conjectural relation between the category of line defects in topologically twisted 3d ${\cal N} = 4$ supersymmetric quantum field theories and categories of modules for Vertex Operator Algebras of boundary local operators for the theories. We test the conjecture in several examples and provide some partial proofs for standard classes of gauge theories.Comment: 57 pages, 8 figure